An electric toy car with a mass of #2 kg# is powered by a motor with a voltage of #4 V# and a current supply of #2 A#. How long will it take for the toy car to accelerate from rest to #3 m/s#?

Question

An electric toy car with a mass of #2 kg# is powered by a motor with a voltage of #4 V# and a current supply of #2 A#.  How long will it take for the toy car to accelerate from rest to #3 m/s#?

Julia Aguilar · Accepted Answer

I tried this:

We can say that the power of the motor will be: #P=VI=4*2=8W# I would then use the theorem of Work #W# and Kinetic Energy #K# to write: #W=DeltaK# #W=1/2mv_f^2-1/2mv_1^2# dividing both sides by the time we get: #1/tW=1/t(1/2mv_f^2-1/2mv_1^2)# #P=1/t(1/2mv_f^2cancel(-1/2mv_1^2))# because the toy car stars from rest (#v_i=0#). so we get: #8=1/t*1/2*2*3^2# rerranging: #t=9/8=1.125s#

Layla Ahmed · Answer

undefined To find the time it takes for the toy car to accelerate from rest to 3 m/s, we can use the equation:

$$ t = \frac{v - u}{a} $$

where $ t $ is the time, $ v $ is the final velocity (3 m/s in this case), $ u $ is the initial velocity (0 m/s since the car starts from rest), and $ a $ is the acceleration.

To find the acceleration, we can use the equation:

$$ a = \frac{F}{m} $$

where $ F $ is the force generated by the motor and $ m $ is the mass of the car.

The force generated by the motor can be calculated using the equation:

$$ F = V \times I $$

where $ V $ is the voltage and $ I $ is the current.

Substituting the given values:

$$ F = 4 \, \text{V} \times 2 \, \text{A} = 8 \, \text{N} $$

Then, we find the acceleration:

$$ a = \frac{8 \, \text{N}}{2 \, \text{kg}} = 4 \, \text{m/s}^2 $$

Now, we can plug the values into the first equation to find the time:

$$ t = \frac{3 \, \text{m/s} - 0 \, \text{m/s}}{4 \, \text{m/s}^2} = 0.75 \, \text{s} $$

So, it will take 0.75 seconds for the toy car to accelerate from rest to 3 m/s.